Let the mass of particle A be m and the mass of particle B be 2m. The displacement equations for particles A and B are:

\(s_A = 30t - 5t^2\)

\(s_B = 15 - 5t^2\)

At collision, \(s_A + s_B = 15\), leading to \(15 = 30t\), so \(t = 0.5\).

At \(t = 0.5\), the velocities are:

\(v_A = 30 - 10 \times 0.5 = 25\) m/s

\(v_B = -10 \times 0.5 = -5\) m/s

Using conservation of momentum:

\(25(2m) - 5(m) = (3m)v\)

\(v = 15\) m/s

For the second case, let the mass of particle A be 2m and the mass of particle B be m:

\(25(m) - 5(2m) = (3m)v\)

\(v = 5\) m/s

The equations of motion for particle C are:

\(s = -13.75 + 15t - 5t^2\)

\(s = -13.75 + 5t - 5t^2\)

Solving for \(t\) when \(s = 0\):

\(t_{C_1} = 3.74\), \(t_{C_2} = 2.23\)

The difference in time is:

\(T = t_{C_1} - t_{C_2} = 1.50\) seconds